How does a monopoly firm determine its price?

Question

BlackTom AI · Accepted Answer

A monopoly sets output where marginal revenue equals marginal cost, then reads the corresponding price off the market demand curve.

Relevant concepts:
- Demand curve P(Q): shows the maximum price consumers will pay for each quantity Q.
- Total revenue TR(Q) = P(Q) · Q.
- Marginal revenue MR(Q) = dTR/dQ = P(Q) + Q·dP/dQ (for a downward‑sloping demand).
- Marginal cost MC(Q): extra cost of producing one more unit.
- Profit maximization requires MR(Q) = MC(Q); the monopolist is a price‑maker but still faces the demand constraint.

Step‑by‑step reasoning (symbolic):
1. Start with demand: P = P(Q).
2. Compute TR: TR(Q) = P(Q) · Q.
3. Differentiate to get MR: MR(Q) = d[ P(Q)Q ]/dQ = P(Q) + Q·P′(Q).
4. Set the profit condition: MR(Q*) = MC(Q*). Solve this equation for the profit‑maximising output Q*.
5. Use the demand curve to find the price: P* = P(Q*). That is, once Q* is chosen to satisfy MR = MC, the firm cannot set a higher price than P(Q*) if it still wants to sell Q*; raising price would reduce quantity demanded.

Why option (a) is correct:
- It precisely states the two‑step process: choose Q* via profit maximization (MR = MC), then use the demand curve to determine the price at which that Q* can be sold. That is the textbook monopoly pricing rule.

Why the other options are incorrect:
- (b) “Charge any price” is false: the monopolist is constrained by the demand curve; arbitrary prices may yield zero sales or lower profit.
- (c) Pricing at minimum average cost is a rule for certain regulatory or long‑run competitive benchmarks, not for monopoly profit maximization; monopolists do not generally price at min AC.
- (d) “Should lower price because demand is elastic” is incomplete/wrong: elasticity affects optimal markup (Lerner index) but does not imply the firm should always lower price; optimal pricing balances MR and MC.

Conclusion: The correct choice is (a), matching the provided answer.

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